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CAT CAT QA — Mixed — practice questions

Explore 43 free CAT QA — Mixed questions in CAT Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.

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CAT QA — Mixed questions and exercises with answers

Showing questions 1–30 of 43.

In how many ways can the letters of the word EQUATION be arranged?Read the answer and worked solution →The number of arrangements of letters of the word MISSISSIPPI is:Read the answer and worked solution →How many 5-digit numbers can be formed using digits 1-9 (no repetition)?Read the answer and worked solution →From 10 boys and 8 girls, a committee of 5 is to be formed with exactly 3 boys. Number of ways:Read the answer and worked solution →Number of ways 4 people can sit at a round table:Read the answer and worked solution →Number of diagonals in a polygon with n sides:Read the answer and worked solution →How many words can be formed using all letters of HELLO?Read the answer and worked solution →The 20th term of the AP 3, 7, 11, 15, ... is:Read the answer and worked solution →Sum of first 50 natural numbers:Read the answer and worked solution →In a GP, if first term is 2 and common ratio is 3, the 8th term is:Read the answer and worked solution →Sum to infinity of the GP 1 + 1/2 + 1/4 + 1/8 + ... =Read the answer and worked solution →If three numbers a, b, c are in AP, then 2b =Read the answer and worked solution →For positive numbers a, b: AM-GM inequality states:Read the answer and worked solution →Sum of squares of first n natural numbers:Read the answer and worked solution →A card is drawn from a deck of 52. Probability it is a face card (J, Q, K):Read the answer and worked solution →Probability of getting at least one head when flipping 3 coins:Read the answer and worked solution →Bag has 5 red, 7 white balls. Two drawn without replacement. P(both red):Read the answer and worked solution →P(A) = 0.6, P(B) = 0.5, P(A ∩ B) = 0.3. P(A | B):Read the answer and worked solution →In a class, 60% pass math and 40% pass English; 25% pass both. Probability student passes math given pass English:Read the answer and worked solution →A binary string of length 5 is randomly chosen. P(exactly 3 zeros):Read the answer and worked solution →If P(A) = 1/3, P(B) = 1/4, A and B are independent. P(A ∪ B):Read the answer and worked solution →In tossing 2 dice, what is the probability that both dice show the same number?Read the answer and worked solution →Arithmetic mean of 5, 8, 10, 12, 15:Read the answer and worked solution →Mode of 4, 5, 4, 6, 4, 7, 5, 4, 8 is:Read the answer and worked solution →For data X = a, a+1, a+2, ..., a+9 (10 consecutive integers), variance:Read the answer and worked solution →Coefficient of variation (CV):Read the answer and worked solution →If each observation multiplied by 3, SD becomes:Read the answer and worked solution →A train travels 360 km in 4 hours. Its average speed:Read the answer and worked solution →Average speed for journey of equal distances at 60 km/h and 40 km/h:Read the answer and worked solution →Compound interest on ₹10000 at 10% per annum for 2 years:Read the answer and worked solution →

Worked practice questions

In how many ways can the letters of the word EQUATION be arranged?

  1. 8! = 40320
  2. 7! = 5040
  3. 8 × 7
  4. 8!/2! = 20160
Show answer and solution

Correct answer: A. 8! = 40320

EQUATION has 8 distinct letters (E,Q,U,A,T,I,O,N — all different). Number of arrangements = 8! = 40320.

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The number of arrangements of letters of the word MISSISSIPPI is:

  1. 11!/(4! × 4! × 2!) = 34650
  2. 11
  3. 11!/4!
  4. 11!
Show answer and solution

Correct answer: A. 11!/(4! × 4! × 2!) = 34650

**MISSISSIPPI has 11 letters:** M(1), I(4), S(4), P(2). **Arrangements with repetition:** 11!/(1! × 4! × 4! × 2!) = 39916800/(1 × 24 × 24 × 2) = 39916800/1152 = 34650.

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How many 5-digit numbers can be formed using digits 1-9 (no repetition)?

  1. 5!
  2. 9P5 = 9!/4! = 15120
  3. 9 × 5
  4. 9⁵
Show answer and solution

Correct answer: B. 9P5 = 9!/4! = 15120

9 choices for 1st digit, 8 for 2nd, ..., 5 for 5th. 9P5 = 9 × 8 × 7 × 6 × 5 = 15120.

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More Quantitative Aptitude topics

Quantitative AptitudeAlgebraProfit and LossRatio and ProportionTime and WorkPercentagesAverages and MixturesDI — Tables